It causes congestion if the city refuses to invest in public transportation - which is more a problem in US cities - though some European cities could be behind on keeping up with changes to different degrees
Yes, it always a balance of factors in the system, but what you're talking about is a higher threshold of capacity already. They've built up to higher rise density in Tokyo and are already managing much higher people movement in core higher density areas than the edges of Paris.
You'd be mistaken. Public transit is extremely crowded in the centre during rush hour.
For example, two regional lines (RER B and D) need to share a tunnel in the middle of the city. They've been investigating digging another one for a long time, but, AFAIK. they haven't found an economical way of doing so. The solution is to try to move people to other lines, but those are already very crowded and I'm not aware of any project to build a new line inside of the city limits.